Turbulent drag reduction by streamwise traveling waves

For a turbulent channel flow with zero-net-mass-flux surface actuation in the form of streamwise traveling waves we develop a model-based approach to design control parameters that can reduce skin-friction drag. In contrast to the traditional approach that relies on numerical simulations and experiments, we use turbulence modeling in conjunction with stochastically forced linearized equations to determine the effect of small amplitude traveling waves on the drag. Our simulation-free approach is capable of identifying drag reducing trends in traveling waves with various control parameters. High-fidelity simulations are used to verify quality of our theoretical predictions.